Question

Qual seria a resposta exata, Tenho duvidas?

Answer 1

Explicação passo-a-passo:

1)

a) - 3 + 6i - (8 - 2i)

- 3 + 6i - 8 + 2i

- 11 + 8i

b) 2 - 4i - 7 + 9i - (- 6 - 3i)

- 5 + 5i + 6 + 3i

1 + 8i

c) (3 + 6i)(- 10 - 4i)

- 30 - 12i - 60i - (24i²)

- 30 - 72i - (24.(-1))

- 30 - 72i - (- 24)

- 30 - 72i + 24

- 6 - 72i

d) (- 1 - i)(- 1 + 4i)

1 - 4i + i - (4i²)

1 - 3i - (4.(- 1))

1 - 3i - (- 4)

1 - 3i + 4

5 - 3i

2)

z² = (- 6 + 9i)²

z² = 36 - 108i + 81i²

z² = 36 - 108i + 81.(-1)

z² = 36 - 108i - 81

z² = - 45 - 108i

3)

$z = \frac{- 8 + 10i}{- 2i} \\\\ z = \frac{- 8}{- 2i} + \frac{10i}{- 2i} \\\\ z = - 5 + 4i \\\\ z(conjug.) = - 5 - 4i$

4)

$z = \frac{(5 + 2i)(2 - i)}{3 + i} \\\\ z = \frac{10 - 5i + 4i - 2i^2}{3 + i} \\\\ z = \frac{10 - i - 2.(-1}{3 + i} \\\\ z = \frac{10 - i + 2}{3 + i} \\\\ z = \frac{12 - i}{3 + i} \\\\ z = \frac{(12 - i)(3 - i)}{(3 + i)(3 - i)} \\\\ z = \frac{36 - 12i + i^2}{9 - i^2} \\\\ z = \frac{36 - 12i - 1}{9 - (- 1)} \\\\ z = \frac{35 - 12i}{9 + 1} \\\\ z = \frac{35 - 12i}{10} \\\\ z = 3,5 - 1,2i$

Espero ter ajudado.